Which is the correct order of the basic strength of given amines?
Step 1: Understanding Basic Strength of Amines
- The basic strength of amines depends on their ability to donate a lone pair of electrons on nitrogen.
- Alkyl groups increase electron density on nitrogen through the +I (inductive) effect, enhancing basicity.
- Aromatic amines have a resonance effect (-R effect), which delocalizes the lone pair of nitrogen into the benzene ring, reducing basicity.
Step 2: Comparing the Given Amines
1. Diethylamine \( (C_2H_5)_2NH \) has two ethyl groups, which exert a strong +I effect, making it the most basic.
2. Ethylamine \( C_2H_5NH_2 \) has only one ethyl group, so it is slightly less basic than diethylamine.
3. Ammonia \( NH_3 \) has no alkyl group, making it less basic than both ethylamine and diethylamine.
4. Aniline \( C_6H_5NH_2 \) has a benzene ring, which withdraws electron density from nitrogen due to resonance (-R effect), making it the least basic.
Step 3: Conclusion
The correct order of basicity is: \[ (C_2H_5)_2NH > C_2H_5NH_2 > NH_3 > C_6H_5NH_2 \]
If the value of \( \cos \alpha \) is \( \frac{\sqrt{3}}{2} \), then \( A + A = I \), where \[ A = \begin{bmatrix} \sin\alpha & -\cos\alpha \\ \cos\alpha & \sin\alpha \end{bmatrix}. \]